A Spectral Method for Coupled Fluid-Kinetic Flow Simulations

We present a spectral method designed to model flows containing both near-continuum and kinetic-dominated regions. The method uses a unified discretization that solves the multispecies Boltzmann equation in all flow regimes. For simplicity, we consider here the Bhatnagar-Gross-Krook model for the collision term, although generalizations are straightforward. Asymmetrically weighted Hermite basis functions provide a spectral expansion of the velocity space and the resulting system of equations for the spectral coefficients is solved using high order finite differences in a highly scalable implementation. The number of terms in the expansion can be adapted based on the local representation error. Thus, near-continuum regions can be captured with the first few moments, while regions with strong kinetic effects require more terms in the expansion. We present verification of the algorithm, demonstrating mathematical correctness and physics simulation capabilities with canonical examples.